Pros
For a chemical or mechanical engineer, you'll get to fully use your education. Entry-level pay is strong versus competitors, the work is challenging, and developmental opportunities are robust. In fact, the executives themselves managed to climb the ladder from the ranks of the engineers so theoretically you can make it to the very top. Employee investment is very front-loaded towards new hires, both in terms of technical training as well as business acumen training. Bonuses are good at Chevron and there's still a pension which is increasingly atypical of employers these days. There are opportunities to develop skills which are valuable outside of Chevron. Take advantage of these. The Data Science and Lean Sigma programs are very underutilized and can make you valuable outside the lumbering dinosaur of Oil & Gas.
Cons
Weak opportunities for non-engineers. If you aren't an engineer, expect to spend your career mostly in the same place and at best climbing the ladder only one or two rungs. Repeated relocations are expected for anyone who wants to climb the ladder. If you are married to someone gainfully employed outside Chevron or are otherwise not positioned to relocate every few years, you'll go nowhere in the long-run. The saying is: "If you don't move, you don't matter". Once you reach mid-career, the opportunities become very limited. Training and development is not really intended to help you. If you haven't been flagged as "high potential" (rare!) then you'll probably stagnate in your current position or within a narrow set of positions. There is no means for asking for a raise. You'll get 3% to 6% in terms of an annual pay increase, most of which is determined by corporate performance rather than your own. This often makes it worthwhile for employees with more than 5 years experience to go elsewhere if the pay increase is substantial or if they're confident in their talents. Under CEO Mike Wirth, Chevron has gone all-in on "woke" politics, in an especially ham-fisted way. If you aren't inclined towards PC culture, you'll need to learn to fake it or at least stay very silent. Race and gender are increasingly major factors in hiring and promotion, which may or may not benefit you.